3
votes
1answer
81 views

How much of mathematics could be created now using computers [closed]

What great mathematical achievements of the previous times could be easily gotten today using computers and heuristic algorithms of CS. I do not mean calculation of constants, but mostly proving ...
2
votes
1answer
85 views

Questions about a computer science field

I would like to have some information about the computer science field, " Algorithmic and Systems Analysis ". Is this a field of theoretical computer science? What subjects are related with this ...
1
vote
3answers
64 views

Which discrete mathematics book to read for a software engineer?

I'm a computer science student, but I lack a good mathematics background. So I decided to start working on that. I was searching in the topic and I found that for computer science a good knowledge of ...
0
votes
1answer
115 views

I want to pursue Computer Science as a major but I don't know if i should…HELP!? [closed]

I'm currently a second semester sophomore who's currently pursuing a Global Affairs major and minoring in Japanese Studies. I plan on going to law school after college and I'm interested in ...
1
vote
2answers
92 views

Which pure mathematical problems could be tackled with an algorithm solving NP-complete problems?

In the past, practical applications have motivated the development of mathematical theories, which then became the subject of study in pure mathematics, where mathematics is developed primarily for ...
3
votes
0answers
65 views

Related paradigms in Computer Science and Mathematics

I've read in a number of places discussions on whether Mathematics is a branch of Computer Science and vice-versa (see here for example) Having a background in both, I know that the Computer Sciences ...
127
votes
14answers
22k views

Is computer science a branch of mathematics?

I have been wondering, is computer science a branch of mathematics? No one has ever adequately described it to me. It all seems very math-like to me. My second question is, are there any books about ...
3
votes
2answers
130 views

What will I be doing?

I'm a freshman studying discrete mathematics B.sc. It's easy to google ''typical mathematician jobs'' and get an idea of what mathematicians do for a living, but what sort of jobs can I expect to work ...
4
votes
0answers
135 views

Math or CS PhD areas to look at. [closed]

I am looking into getting back to school to get a PhD in Mathematics or Computer Science (I hold MA in Math). I am wondering what new areas of research in Math and CS are promising in a sense that ...
3
votes
4answers
231 views

Mathematics for Computer Science

What are the various forms of mathematics that may be required in a computer scientist career? Say someone one day wants to prove things like P vs. NP, and meanwhile be writing advacned algorithms for ...
1
vote
3answers
108 views

how can we write abstract algorithms?

Writing pseudo-code for algorithms is common practice in the applied mathematics literature. It is also often the case that the ideal input of an algorithm is an infinite set, for example it could be ...
24
votes
4answers
716 views

Why do we believe the Church-Turing Thesis?

The Church-Turing Thesis, which says that the Turing Machine model is at least as powerful as any computer that can be built in practice, seems to be pretty unquestioningly accepted in my exposure to ...
4
votes
2answers
280 views

Going back to the basics? [closed]

I'm currently in my second year of college majoring in comp sci and I haven't really taken any math courses yet except pre-calc. In high school, I thought of myself as a pretty good math student and ...
6
votes
4answers
247 views

What is the relationship between “recursive” or “recursively enumerable” sets and the concept of recursion?

I understand that "recursive" sets are those that can be completely decided by an algorithm, while "recursively enumerable" sets can be listed by an algorithm (but not necessarily decided). I am ...
0
votes
1answer
90 views

Why do we need tactics, reflection and other techniques when we have Curry-Howard for theorem proving?

First of all, I apologize if this question is slightly misplaced, but this seemed the best place to ask it given the mathematical/theoretical nature of the discussion. Given that the Curry-Howard ...
1
vote
0answers
87 views

Historical relation between computer science and the theory of dynamical systems

I wonder if there is any historical relation between the fields of Dynamical systems (and related fields such as Optimal control) and (theoretical) Computer science. The reason for which I ask this ...
5
votes
4answers
402 views

How to start with automated theorem proving?

I'm interested in this question, but I'm not going to list my knowledge/demands but rather gear it to more general purpose; so the first thing concerns the prerequisites, i.e. How much ...
3
votes
1answer
228 views

Proving NP-completeness intuition

When approaching a problem in NP, initially not knowing whether the problem is in P or NP-complete (or some other choice). It seems to me the only way one can go about "solving" this problem is to ...
6
votes
1answer
169 views

State of the progess of the automated proof checking

I recently came across a concept of automated proof checking. I am very intrigued by the idea, that in the future all the proofs could be verified by a computer. Moreover, some proofs were already ...
4
votes
2answers
2k views

Computational complexity of computing the determinant

The formula for the determinant of an $n$ by $ n$ matrix given by expansion of minors involves $n!$ terms. As such, computing the determinant of a given matrix of with integer entries via expansion by ...
3
votes
4answers
359 views

Mathematics necessary for a Master's degree in CS

I'm contemplating doing a Master's degree in Computer Science at night school. What sort of mathematics am I likely to encounter?
2
votes
1answer
486 views

Considering math or computer science

Let me start by saying I graduated High School in 2002 and have worked as a technician, a systems administrator, and a part time web developer up till now. I have started taking courses at community ...
1
vote
2answers
3k views

Understanding $\epsilon$ transitions in a finite state automaton

I am trying to understand how $\epsilon$ transitions work. From what I've read, when you "go" to a state S that has arrows pointing outwards with $\epsilon$'s in it, you automatically go to those ...
2
votes
1answer
80 views

a function of a dependent type, a section, a sheaf

I have defined this simple sheaf. Take $E:set, B:set, p:E\to B$. Let $P(B)$ be a set of subsets of $B$. Let $S$ be the set of sections of $p$. Let $F$ be a contravariant functor from $P(B)$ as a poset ...